# Math 10 Week 18

THE 5 MOST FUN THINGS IN GR.10

This is the last blog post I will be doing for Math 10 and it hurts me to say that. This year I loved Math. Every Unit was challenging and I think it was a big step up from grade 9. At the beginning of the year I wanted a challenge and I for sure got one. Math 10 is very important. The next two years are going to build off of what I learned this year so it’s important to know what you need to work on for the following years. I am going to state the 5 most important things I think were the most enjoyable this year.

1. DO YOUR HOMEWORK- This may not be fun… But it is Super important. And yes, I still need to work on getting better at this, but it is the most important thing for any class. You need to start making good work habits ASAP.
2. The second favorite part for me was doing SYSTEMS OF LINEAR EQUATIONS. I just loved how i could feel so confident in my answer because I could verify. I loved understanding how an equation could work and how I could get answers i never thought I could. I knew more about an equation than I thought.
3. The third thing is TRIGONOMETRY. It was by far the easiest unit for me. It was a little bit tricky in some parts but for the most part it was easy. If you pay attention you do great.
4. Number four was FACTORING AND POLYNOMIAL EXPRESSIONS. This one was my favorite because I got an incredible mark on my test that I was not expecting. I was just really proud of myself.
5. The last thing on my list was THE PEOPLE IN MY MATH CLASS. I could have not asked for a better math 10 class. Everyone was so kind. It was so much fun when everyone took the  projects we did seriously. I loved when I could teach someone something and they could teach me something. I just loved hoe everyone contributed so well.

Math 10 was amazing for me and I would do it again. A big Thank You goes out to the greatest math teacher I’ve had in a long time. Mrs. Burton, thank you for teaching me so much and making it fun. I was a little nervous because I heard from other people it was going to be hard but you helped me get my way through it. 🙂

# Math 10 Week 17

This week in math 10 I learned how to use substitution in equations

ex. $\frac{1}{2}$ x – y = 3          2x – 5y = -7

There are 5 Steps:

Step 1: Choose the simplest equation and isolate on of the variables.

Step 2: Substitute the answer from step one into the other equation

Step 3: Solve the single variable equation

Step 4: Substitute the answer from step 4 into the original equation in step one to find the value of the other variable

Step 5: Verify

# Math 10 Week 16

This week I learned how to convert                                                         between different forms of equations of a line. I also thought it would be important to teach you how to find the y and x axis intercepts if you don’t already know.

Ex. (-2, 5) (4, -13)

Point Slope Form:                         m(x – x1)= y-y1

General Form: Ax+By+C=0

Slope-y Intercept Form: y=mx + b

• m is the slope
• b is what you’re going to be isolating
• b is also what the y intercept is going to be
• The x and y in the equation is going to be taken from one group of coordinates

You need to know the slope for this form, the slope is -3

I’m going to choose (-2, 5) for my x and y coordinates in the equation you also need to simplify

The y intercept is -1 (this is the b in the y=mx + b)

Slope-y intercept form is: y= -3x -1

To convert from Slope y Intercept to General Form: Ax+By+C = 0

• All you need to do is move y to the side where x is positive and if x is not positive then you move everything on the -Ax side to the y side.

Point Slope Form : m(x – x1)= y-y1

• Super fast and easy

All of the equations mean the same thing and get the same line.

# Math Initials Assignment: JP

This week we had to do an                                                                               assignment. On Desmos we had to put points on a graph that spelled our initials out. We needed to write the equation for each line and include the Domain and range. We had to at least write one equation in Slope y Intercept Form, General Form and Point Form.

Slope y Intercept Form: y= mx + b

General Form: Ax + By + C =0

Point Form: m( x – x1 ) = y – y1

Here are the tables I used to plot the points/make my initials on my graph:

Here are my equations for each line segment:

Here is all of my work:

# Math 10 Week 15

This week our class learned about slope. Slope means how steep a line is.

To find the steepness of the line segment we use $\frac{Rise}{Run}$ .

To help find the slope choose two nice points from the line segment. Rise is how high is goes (y) and Run is how far is travels (x).

In this image the slope is $\frac{2}{3}$ . That is because The rise (y) goes up to and the run (x) goes over three. This will also be positive because the line segment is moving upwards. We read the lines/graphs from left to right and this line goes from bottom up. For the line to become negative it would have to being going downwards from left to right. then the slope would be $\frac{-2}{3}$ .

I will also introduce this handsome guy.

His name is Mr. Slope Guy and he helps us understand lines better.

The green features of his face represent a positive line.  Notice if we read from left to right the line travels up

The red represents a negative line segment.notice if we read from left to right the line segment goes downward

His nose represents a vertical line. It has a little U under the line  to help us remember the word undefined.

His mouth is the Zero Slope Line. It means that a horizontal line segment is 0. This is because it has no slope, so the slope is 0. Y needs to be higher or lower than 0 but cannot be 0!

# Math 10 Week 14

This week we learned how to find the length of of a line segment. This takes place in graphing. It is from one coordinate to another.

ex. Say the coordinates are x1 and y1 (2, -10) and (4,8) x2 and y2

To find the length of a line segment you need to use the formula of $(x1-x2) ^2$ + $(y1-y2) ^2$ = $C^2$

$(2-4)^2$ + $(-10 - 8)^2$$C^2$

$-2^2$$-18^2$$C^2$

You are doing this step because of pythagoras

4 + 324 = $C^2$

$\sqrt{328}$ = $C^2$

The length of the line segment is roughly 18.1

# Math 10 Week 13

This week I learned how to tell the difference between a relation and a function. A relation has more than one possibly y for x, and a function is special and only has one y for x.

I am going to show you what functions and relations look like.

Functions & Relations

Another thing I thought was important  to know how to to do was  a question like f(x)=1- $x^2$

# Math 10 Week 12

This week we started Relations and Functions. This is something i think would be helpful remembering.

Relation: A comparison between two sets of elements (numbers) is a relation.

Ex. The cost of pellets is related to the weight.

To determine which is the input or the output you need to remember which one depends on which.

It does not make sense for the weight to depend on the cost therefore the sentence should be written as the cost depends on the weight. Because of this the cost is the input also known as the dependent, y and range. The weight is known as the independent, the input, and the domain.

There are 5 different relations.

Table of Values

Ordered Pairs

A Mapping diagram

An Equation

Graph

# Math 10 Week 11

This week I will be teaching you how to factor an ugly polynomial. When I say an ugly polynomial it just means that the leading coefficient isn’t 1.

Ex. $6x^2$ + 7x +2

Step 1: Break down the leading coefficient, then start writing it out

6=2 x 3                                  (3x___)(2x___)

Step 2: Play around with the factors of the constant to find out the appropriate spot that will multiply and then add to 7.

*Th object is to get the middle term.

(3x + 2)(2x +1)                   *2 and 2x will multiply=4x        *3x and 1 will multiply= 3x

3x + 4x = 7x

Pictures below

# Math 10 Week 10

This week I learned how to factor a simple polynomial. A simple polynomial means the leading coefficient is a one. To factor a simple polynomial you need to know what factoring is. Factoring is finding all the different numbers that multiply to get a certain number. Ex. 24 the factors of 24 are 1,2,3,4,6,8,12,24. Now I can teach you how to factor a simple polynomial.

Ex. $x^2$ + 8x +12

Step one: Factor the constant.

Step Two : Look at the clues; which of the pairs subtract or add to give you the middle term.

In this case it would be 2 and 6. Another clue is that everything is positive so the factors will be positive.

Step Three: Start writing it out

*You know that x times x is $x^2$ so the x’s will go at the front of the brackets. (x___)(x___)

The answer is (x +2) (x +6)

To check your answer use the claw method.

THERE IS A VIDEO BELOW TO SHOW YOU HOW TO USE THE CLAW METHOD, ALSO KNOWN AS FOIL